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2 years ago

13

Mrs.Giblin begins hiking at mile marker 25 on the Appalachian Trail and hikes 3 miles every hour. What is the slope?

1 answer:

Ilya [14]2 years ago

7 0

Answer:

3 miles

Step-by-step explanation:

Slope is simply the change in position per unit rate. We could conclude that the steepness of the Applachian is the rate of change in position per unit time. Since the distance hiked on the Applachian is said to be 3 miles per hour, then we can conclude that the slope of the applachian is 3 miles

This is the change in miles / change in time.

Chang in miles = 3

Change in time = 1

Slope = 3/1

Slope = 3

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Ivan

Answer:

$\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}$

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

<u>Given</u><u> </u><u>:</u><u>-</u>

• $\sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}$

<u>To</u><u> </u><u>Prove</u><u> </u><u>:</u><u>-</u><u> </u>

• $\sf\implies cos2A =\dfrac{\sqrt3}{2}$

<u>Proof </u><u>:</u><u>-</u><u> </u>

We know that ,

$\sf\implies cos2A = 1 - 2sin^2A$

Therefore , here substituting the value of sinA , we have ,

$\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2$

Simplify the whole square ,

$\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8}$

Add the numbers in numerator ,

$\sf\implies cos2A = 1-2\times \dfrac{4-2\sqrt3}{8}$

Multiply it by 2 ,

$\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4}$

Take out 2 common from the numerator ,

$\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4}$

Simplify ,

$\sf\implies cos2A = 1 -\dfrac{ 2-\sqrt3}{2}$

Subtract the numbers ,

$\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2}$

Simplify,

$\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} }$

Hence Proved !

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